I can't actually find a calculator that will give me the numbers past 8 sigmas, which is 6.61 x 10 ^-16.

Given the way that curve runs, a 25-sigma event is best described as something that is "impossible;" never going to happen; way, way, way beyond the fabled "black swan." In fact, I feel 100% confident in saying (with apologies to Wayne and Garth) that we are far more likely to see a real black swan fly out of Mr. Viniar's posterior than we (or he) are to see a single 25-sigma event, much less several of them in a row.

In other words, Goldman's models were saying that something that couldn't ever happen was happening. Incredibly, most of Wall Street used this as an example of how unprecedented the financial crisis was, rather than an example of how faulty its models were.

I recently interviewed Nobel Prize-winning economist Joseph Stiglitz in his office at Columbia Business School. In this clip, Stiglitz discusses the errors in Wall Street's risk models. Have a look (transcript follows):

Stiglitz: The simple models didn't focus adequately on the extreme events. They assume nice probability distributions, which underestimated the likelihood of these unusual events. And as several people have remarked, events that were supposed to happen once in a lifetime of the universe were happening every ten years. And we laugh at things like that happening. You should say, Something's wrong with our model. They didn't say that. They tried to tweak the model a little bit, but they didn't really address the fundamental flaw.

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